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Base change along the Frobenius endomorphism and the Gorenstein property

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Let $R$ be a local ring of positive characteristic and $X$ a complex with nonzero finitely generated homology and finite injective dimension. We prove that if derived base change of… Click to show full abstract

Let $R$ be a local ring of positive characteristic and $X$ a complex with nonzero finitely generated homology and finite injective dimension. We prove that if derived base change of $X$ via the Frobenius (or more generally, via a contracting) endomorphism has finite injective dimension then $R$ is Gorenstein.

Keywords: base change; change along; endomorphism; base; along frobenius

Journal Title: Journal of Algebra
Year Published: 2021

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